The Penny-Shaped Crack and the Plane Strain Crack in an Infinite Body of Power-Law Material

[+] Author and Article Information
M. Y. He

Institute of Mechanics, Chinese Academy of Sciences, Beijing, China

J. W. Hutchinson

Division of Applied Sciences, Harvard University, Cambridge, Mass. 02138

J. Appl. Mech 48(4), 830-840 (Dec 01, 1981) (11 pages) doi:10.1115/1.3157742 History: Received March 01, 1981; Online July 21, 2009


A study is carried out of the problem of a penny-shaped crack in an infinite body of power-law material subject to general remote axisymmetric stressing conditions. The plane strain version of the problem is also examined. The material is incompressible and is characterized by small strain deformation theory with a pure power relation between stress and strain. The solutions presented also apply to power-law creeping materials and to a class of strain-rate sensitive hardening materials. Both numerical and analytical procedures are employed to obtain the main results. A perturbation solution obtained by expanding about the trivial state in which the stress is everywhere parallel to the crack leads to simple formulas which are highly accurate even when the remote stress is perpendicular to the crack.

Copyright © 1981 by ASME
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